PhpStom + XDebug + Codeigniter (MVC)
Accordingly to your comment .. the problem seems to be in incorrect value of "Host" field in Settings | PHP | Servers (1st screenshot) -- it should be just domain/host name and not actual URL (compare with "Server name" filed on 3rd screenshot) -- just remove /~*** part. The path mappings seems to be set up correctly.
Alternatively -- just delete any entries in Settings | PHP | Servers and use Zero-Config approach -- IDE will help setting it up on first successful debug connection.
As for 3rd screenshot -- IDE behaves correctly. Because there is no correct path mapping (with correct server/host name) PhpStorm breaks at first line of currently running script, which is index.php (entry point into your MVC application). Once correct path mapping will be established, IDE will be stopping on breakpoints only (unless it matches some criteria in "Settings | PHP | Debug | Xdebug" section).